Question Number 66245 by aliesam last updated on 11/Aug/19 $${prove}\:{that} \\ $$$$ \\ $$$$\int{e}^{{x}} \:{dx}\:=\:{e}^{{x}} \:+\:{c} \\ $$ Commented by Rio Michael last updated on…
Question Number 697 by 123456 last updated on 02/Mar/15 $${given}\:{that}\:\frac{\mathrm{1}}{\sigma\sqrt{\mathrm{2}\pi}}\underset{−\infty} {\overset{+\infty} {\int}}{e}^{−\frac{\left({t}−\mu\right)^{\mathrm{2}} }{\mathrm{2}\sigma^{\mathrm{2}} }} {dt}=\mathrm{1} \\ $$$${and}\:{g}\left({n},{u}\right)=\frac{\mathrm{1}}{\sigma\sqrt{\mathrm{2}\pi}}\:\underset{−\infty} {\overset{+\infty} {\int}}\left({x}−{u}\right)^{{n}} {e}^{−\frac{\left({t}−\mu\right)^{\mathrm{2}} }{\mathrm{2}\sigma^{\mathrm{2}} }} {dt} \\ $$$${and}\:{f}\left({n},{u}\right)=\frac{\mathrm{1}}{\sigma\sqrt{\mathrm{2}\pi}}\underset{−\infty}…
Question Number 689 by 112358 last updated on 25/Feb/15 $${Evaluate}\: \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} {sin}\left({x}^{\mathrm{2}} \right){dx}, \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} {cos}\left({x}^{\mathrm{2}} \right){dx}, \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\infty} {tan}\left({x}^{\mathrm{2}} \right){dx}.…
Question Number 66213 by mathmax by abdo last updated on 10/Aug/19 $${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{{n}} \right){dx}\:{and}\:{B}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{{n}} \right){dx} \\ $$$${with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{2} \\ $$ Commented…
Question Number 131743 by frc2crc last updated on 08/Feb/21 $$\underset{{C}:\mid{z}\mid=\mathrm{1}} {\int}\frac{−\mathrm{2}{i}}{{Az}^{\mathrm{2}} +\mathrm{2}{z}+{A}}{dz}\:{where}\:{C}\:{is}\:{a}\:{unit}\:{circle}\:{with}\:{radius}\:\mathrm{1} \\ $$ Answered by mathmax by abdo last updated on 08/Feb/21 $$\mathrm{let}\:\varphi\left(\mathrm{z}\right)=\frac{−\mathrm{2i}}{\mathrm{az}^{\mathrm{2}} \:+\mathrm{2z}+\mathrm{a}}\:\mathrm{poles}\:\mathrm{of}\:\varphi?…
Question Number 66194 by aliesam last updated on 10/Aug/19 $$\int\frac{{x}^{{a}} }{{bx}^{{n}} +{c}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131711 by mnjuly1970 last updated on 07/Feb/21 $$\:\:\:\:\:\:\:{advanced}\:\:{cslculus}\:.. \\ $$$$\:\:{prove}\:\:{that}: \\ $$$$\:\:\underset{{n}=\mathrm{0}\:} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{16}^{{n}} }\left(\frac{\mathrm{4}}{\mathrm{8}{n}+\mathrm{1}}−\frac{\mathrm{2}}{\mathrm{8}{n}+\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{8}{n}+\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{8}{n}+\mathrm{6}}\right)=\pi \\ $$ Commented by JDamian last updated on…
Question Number 66170 by mathmax by abdo last updated on 10/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{sin}\left({x}^{\mathrm{3}} \right){dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 66168 by mathmax by abdo last updated on 10/Aug/19 $${prove}\:{without}\:{calculus}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}=\int_{\mathrm{0}} ^{\infty} {sin}\left({x}^{\mathrm{2}} \right){dx} \\ $$ Terms of Service Privacy Policy…
Question Number 66169 by mathmax by abdo last updated on 10/Aug/19 $${find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}\:{and}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{\mathrm{2}} \right){dx}\left({fresnel}\:{integrals}\right) \\ $$$${by}\:{using}\:\Gamma\left({z}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{z}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\: \\…